Packed Bed Reactor with "Extra Dimension"

Packed Bed Reactor with "Extra Dimension" An extra dimension approach to model the mass and reaction distributon along the reactor and within each catalyst pellet along the reactor length. The pellet radial dimenstion constritutes the extra 4th dimension. Outflow Mass transport in pellet Mass transport in reactor With boundary conditions rp Pellet with radius rp Inflow 0.01 m/s CA=1 mol/m3, CB=0 mol/m3

Before starting to build the model enable the Extra Dimensions option, For that go to The Preferences Dialog Box. Click Model Builder, select the Enable technology preview functionality check box, and then click OK.

Step 1: Define Parameters & Variables Load .txt files

Step 2: Add Extra Dimension and Attach Dimensions Right Click to Component 1 to add Extra dimension, choose 1D for pellet Right Click Component1>Definitions And choose Extra Dimensions>Attached Dimensions

Step 3: Create geometry of packed bed reactor

Step 4: Create geometry for extra dimension which is a 1D for normalized pellet radius Note that x=0 represent the center of pellet and x=1 is the surface of the pellet

Step 5: Meshing Extra dimension geometry Mesh the extra dimension geometry Using the above values for size node

Step 6: Meshing the PBR geometry Use structure meshes by combining triangular with swept meshes There are 5 elements in the swept direction

Step 7: Assign Material Property and choose water from add materials node

Step 8: Define Physics Darcy Law for fluid flow Assign porosity and permeability in matrix properties for packed bed

Step 9: Darcy Law Outlet = atmospheric pressure

Step 10: Darcy Law Inlet pressure as 1.1[atm]

Step 11: Add Transport of Dilute Species with number of dependent variable as 2 (A & B) Assign Diffusion coefficient of A & B inside the packed bed column

Step 12: Activate Advanced Physics Options

Step 13: Right Click chds interface and choose weak contribution

Step 14: Within weak contribution Select all domain in both Domain Selection and Extra Dimension 1 Make sure to choose “Attached Dimensions 1” in “Extra Dimension attachment” Right following weak expression for diffusion and reaction of specie A and B in the pellet 4*pi*N*R*r^2*(-DAp*pellet_CAr*test(pellet_CAr)-DBp*pellet_CBr*test(pellet_CBr)+R^2*(react*test(pellet_CB)-react*test(pellet_CA)))

Step 15: Make sure the first spatial coordinates is “r” for the Extra dimension this is because The weak expression is has gradient term that is in r-direction

Step 16: Define Auxiliary Variable, right click Weak Contribution 1 Field Variable name is “pellet_CA” this is the concentration of A inside the pellet

Step 17: Define Auxiliary Variable, right click Weak Contribution 1 Field Variable name is “pellet_CB” this is the concentration of B inside the pellet

Step 18: Add pointwise constraint 1 to couple concentration from pellet to the column Note: The concentration at the surface of the particle is equal to the concentration outside the particle compensated to account for the part of the particle volume that is occupied by solid catalyst support.

Step 19: Add pointwise constraint 2 to couple concentration from pellet to the column

Step 20: Add Inflow boundary condition, Only specie A comes in A is converted to B from reaction inside the pellet A ---> B

Step 21: Add Outflow boundary condition

Step 22: Two step study is used in the model Step 1 solves for Darcy Flow Step 2 solves for mass transport of A & B

Step 23: Results: Plotting concentration inside the pellet along the 3D reactor Make a duplicate of solution 1 Under Data Sets Change the Component to Extra Dimension 1 in the setting window

Step 24: Add 1d Plot group and make sure the Data set is selected as Solution 3

Step 25: Add Line Plot and Type the following expression “comp1.atxd3(0,0,0.1,pellet_CA)” This gives concentration of A inside pellet at position z=0.1 in the column Similar line plot is added for concentration of B

Step 26: Results: Volume plot of concentration of A in the entire reactor

Packed Bed Reactor with "Extra Dimension"